1. Field of the Invention
This invention relates generally to the field of geophysical prospecting and particularly to the field of marine seismic surveys. More particularly, the invention relates to imaging of marine seismic data.
2. Description of the Related Art
In the oil and gas industry, geophysical prospecting is commonly used to aid in the search for and evaluation of subterranean formations. Geophysical prospecting techniques yield knowledge of the subsurface structure of the earth, which is useful for finding and extracting valuable mineral resources, particularly hydrocarbon deposits such as oil and natural gas. A well-known technique of geophysical prospecting is a seismic survey. In a land-based seismic survey, a seismic signal is generated on or near the earth's surface and then travels downwardly into the subsurface of the earth. In a marine seismic survey, the seismic signal may also travel downwardly through a body of water overlying the subsurface of the earth. Seismic energy sources are used to generate the seismic signal which, after propagating into the earth, is at least partially reflected by subsurface seismic reflectors. Such seismic reflectors typically are interfaces between subterranean formations having different elastic properties, specifically wave velocity and rock density, which lead to differences in elastic impedance at the interfaces. The reflections are detected by seismic sensors at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes. The resulting seismic data is recorded and processed to yield information relating to the geologic structure and properties of the subterranean formations and their potential hydrocarbon content.
Appropriate energy sources may include explosives or vibrators on land and air guns or marine vibrators in water. Appropriate types of seismic sensors may include particle velocity sensors in land surveys and water pressure sensors in marine surveys. Particle displacement, particle acceleration sensors, or pressure gradient sensors may be used instead of particle velocity sensors. Particle velocity sensors are commonly know in the art as geophones and water pressure sensors are commonly know in the art as hydrophones. Both seismic sources and seismic sensors may be deployed by themselves or, more commonly, in arrays.
In a typical marine seismic survey, a seismic survey vessel travels on the water surface, typically at about 5 knots, and contains seismic acquisition equipment, such as navigation control, seismic source control, seismic sensor control, and recording equipment. The seismic source control equipment causes a seismic source towed in the body of water by the seismic vessel to actuate at selected times. Seismic streamers, also called seismic cables, are elongate cable-like structures towed in the body of water by the seismic survey vessel that tows the seismic source or by another seismic survey ship. Typically, a plurality of seismic streamers are towed behind a seismic vessel. The seismic streamers contain sensors to detect the reflected wavefields initiated by the seismic source and reflected from reflecting interfaces. Conventionally, the seismic streamers contain pressure sensors such as hydrophones, but seismic streamers have been proposed that contain water particle motion sensors such as geophones, in addition to hydrophones. The pressure sensors and particle velocity sensors may be deployed in close proximity, collocated in pairs or pairs of arrays along a seismic cable.
The sources and streamers are submerged in the water, with the seismic sources typically at a depth of 5-15 meters below the water surface and the seismic streamers typically at a depth of 5-40 meters. Seismic data gathering operations are becoming progressively more complex, as more sources and streamers are being employed. These source and streamer systems are typically positioned astern of and to the side of the line of travel of the seismic vessel. Position control devices such as depth controllers, paravanes, and tail buoys are used to regulate and monitor the movement of the seismic streamers.
Alternatively, the seismic cables are maintained at a substantially stationary position in a body of water, either floating at a selected depth or lying on the bottom of the body of water. In this alternative case, the source may be towed behind a vessel to generate acoustic energy at varying locations, or the source may also be maintained in a stationary position.
Although modern 3D marine seismic acquisition systems with up to sixteen streamers may acquire a large distribution of offsets and azimuth for every midpoint position, available parameter determination techniques (e.g. semblance stacks in different configurations) do not allow for effective azimuth-dependent moveout analysis. Those parameters (i.e. azimuthal velocities), extracted from a general reflection time function, can be of great significance towards a better time imaging; a time imaging beyond the conventional model limitation (i.e., horizontal layering of homogeneous layers along with a vertical velocity gradient). However, this better imaging requires wide or multi-azimuth seismic data acquisition and truly three-dimensional velocity analysis, that is, azimuthal velocity analysis.
The deficiencies in current velocity analysis are due to the small number of traces with higher azimuth and reduced offset in the cross line direction. Thus, there exists a need to develop effective migration techniques that work effectively in three-dimensional media that is not just simply-layered and homogeneous. This need has led to work in determining effective approximations for traveltime functions for transmitted and reflected rays and their corresponding normal moveout and migration velocities.
Ursin, B., 1982, “Quadratic wavefront and travel time approximations in inhomogeneous layered media with curved interfaces”, Geophysics, 47, 1012-1021 describes a quadratic approximation for the square of the traveltime from source to receiver in three-dimensional horizontally-layered media. Ursin 1982 determines that its hyperbolic traveltime approximations are superior to its parabolic approximations.
Bortfeld, R., 1989, “Geometrical ray theory: Rays and traveltimes in seismic systems (second order of approximation of the traveltimes)”, Geophysics, 54, 342-349 describes second-order parabolic approximations for the traveltimes of transmitted and reflected rays in layered media with constant velocities.
Schleicher, J., Tygel, M., and Hubral, P., 1993, “Parabolic and hyperbolic paraxial twopoint traveltimes in 3D media”, Geophysical Prospecting, 41, 495-513 describes second-order parabolic or hyperbolic approximations for the traveltimes of rays in the vicinity of a known central ray in laterally inhomogeneous isotropic layered media. Hubral, P., Schleicher, J., and Tygel, M., 1993, “Three-dimensional primary zero-offset reflections” Geophysics, 58, 692-702, further describe how integration of one-way dynamic ray tracing, instead of two-way integration, suffices to determine factors such as the geometrical-spreading factor that effect zero-offset reflection amplitudes, the reflector Fresnel zone, and a normal moveout velocity.
Grechka, V. and Tsvankin, I, 1998, “3-D description of normal moveout in anisotropic inhomogeneous media”, Geophysics, 63, 1079-1092, and Grechka, V., Tsvankin, I. and Cohen, J. K., 1999, “Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media”, Geophysical Prospecting, 47, 117-148 describe a solution for the normal moveout (NMO) velocity in vertically inhomogeneous, anisotropic media through solving the Christoffel equation for slowness vector parameters or through a generalized Dix equation approach to rms averaging of layer NMO velocities.
Söllner, W., 1996, “Time migration decomposition: A tool for velocity determination” 66th Annual International Meeting., SEG, Expanded Abstracts, 1172-1175 describes a method for determining interval velocities by time migration-decomposition of zero offset stacked traces. Söllner 1996 uses the methodology described in Bortfeld 1989, above.
Söllner, W. and Yang, W-Y., 2002, “Diffraction response simulation: A 3D velocity inversion tool”, 72nd Annual International Meeting, SEG, Expanded Abstracts, 2293-2296 describes a method for determining zero offset diffraction point responses in three-dimensional laterally heterogeneous media. The method needs only normal moveout velocities and zero offset reflection time slopes from the stacked data cube.
Söllner, W., Anderson, E., and Jostein Lima, 2004, “Fast time-to-depth mapping by first-order ray transformation in a 3-D visualization system”, 74th Annual International Meeting., SEG, Expanded Abstracts, describes a method for applying a Runge-Kutta solver to a first-order approximation of ray transformation matrices as described in Bortfeld 1989, above.
Söllner, W. and Anderson, E., 2005, “Kinematic time migration and demigration in a 3D visualization system”, Journal of Seismic Exploration, 14, 255-270 describes three-dimensional kinematic time migration based on azimuthal NMO stacking velocities and zero offset time slopes. Söllner et al. 2005 further describes kinematic time demigration based on azimuthal time migration velocities and time migration slopes. Both processes are derived for three-dimensional media with mildly-dipping layers with weakly-varying velocities and smoothly curved interfaces.
Martinez, R. and Sun, C., 2004, “3D Prestack Time Migration Method”, U.S. Pat. No. 6,826,484 B2, describes a Kirchoff-type time migration using a weighted diffraction stack in horizontally-layered, transversely isotropic media with a vertical symmetry axis (VTI).
As the azimuthal dependency of time velocities can either be caused by anisotropy, by inhomogeneity, or both together, then azimuthal velocity analysis should also be based on a general heterogeneous, anisotropic model. Thus, a need exists for azimuthal velocity analysis that allows time migration that is effective in general heterogeneous, anisotropic media.